Divide. Express your answer in simplest form.

2 1/2 ÷ 2 1/6

The events of choosing a jack or a spade out of a standard deck of cards are not mutually exclusive.

Mutually exclusive events are events that cannot happen at the same time. In other words, if one event occurs, the other cannot.

In a standard deck of cards, there are four jacks and thirteen spades. One of the jacks is also a spade (the jack of spades). Therefore, it is possible to choose a card that is both a jack and a spade at the same time.

Since the events are not mutually exclusive, the probability of choosing a jack or a spade is the sum of the probabilities of each event minus the probability of both events occurring:

P(jack or spade) = P(jack) + P(spade) - P(jack and spade) = 4/52 + 13/52 - 1/52 = 16/52 = 4/13

Therefore, the events of choosing a jack or a spade out of a standard deck of cards are not mutually exclusive.

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The velocity of the ball after 2 seconds is 412 feet per second.

The position function for free-falling objects is s(t) = -16t^2 + v0t + S0, where t is the time, v0 is the initial velocity, and S0 is the initial position. In this case, the initial velocity v0 is -19 feet per second and the initial position S0 is the top of a 482-foot building.

To find the velocity after 2 seconds, we can plug in the time t = 2 into the equation and solve for the velocity v:

s(t) = -16t^2 + v0t + S0

s(2) = -16(2)^2 + (-19)(2) + 482

s(2) = -32 -38 + 482

s(2) = 412

Therefore, the velocity of the ball after 2 seconds, after calculation, is 412 feet per second.

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The equation which accurately represents the statement as given are; 4.9x - (-3) = 12.8; 3 + 4.9x = 12.8; and 12.8 = 4.9x + 3.

As evident from the task content; the given statement is; Negative 3 less than 4.9 times a number, x, is the same as 12.8.

Therefore, we have ;

4.9x - (-3) = 12.8

Or by evaluation;

3 + 4.9x = 12.8

Or by rearrangement;

12.8 = 4.9x + 3.

On this note, the equations which represent the given word phrase are; 4.9x - (-3) = 12.8; 3 + 4.9x = 12.8; and 12.8 = 4.9x + 3.

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The magnitude of the electric force upon an electron at point B is 8.16 x 10^-20 N, and it would accelerate in the direction opposite to the electric field, or -7.

The upon an electron at point B can be calculated using the formula F = qE, where F is the force, q is the charge of the electron, and E is the electric field magnitude. The charge of an electron is 1.6 x 10^-19 C, and the electric field magnitude at point B is 0.51 V/m. Therefore, the magnitude of the electric force is:

F = (1.6 x 10^-19 C) (0.51 V/m) = 8.16 x 10^-20 N

To determine the direction in which the electron would accelerate at point B, we need to consider the direction of the electric field. The electric field direction at point B is not given in the table, but we can assume that it is the same as the direction at point A, which is 7.

Therefore, the electron would accelerate in the direction opposite to the electric field, or -7.

The vector indicating the direction in which the electron would accelerate at point B can be drawn as follows:

<--- (electron)

In conclusion, the magnitude of the electric force is 8.16 x 10^-20 N, and it would accelerate in the direction opposite to the electric field, or -7.

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To make 20 litres of the cranapple mixture, Taylor should combine 8 litres of apple juice and (20 - 8) = 12 litres of cranberry juice.

Let's assume that Taylor mixes x liters of apple juice and (20 - x) liters of cranberry juice to make 20 liters of the cranapple mixture.

The price of the used apple juice is $0.85 and the price of the used cranberry juice is $1.25 (20 - x).

The mixture is supposed to be sold for exactly what the ingredients cost, or $1.09 per litre, according to the problem. As a result, the total cost of the juice used to create the mixture must be equivalent to the price at which it is sold.

[tex]0.85x + 1.25(20 - x) = 1.09(20)[/tex]

[tex]0.85x + 25 - 1.25x = 21.8-0.4x = -3.2x = 8[/tex]

Verification:

[tex]0.85(8) + 1.25(12) = 10.8[/tex]

Verify:

1.09(20) = 21.8

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Answer:

See below.

Step-by-step explanation:

We are asked to find the volume of the cereal box.

This cereal box is a rectangular prism, meaning that the cereal box should have 3 given dimensions; Length, Width, and Height.

[tex]Volume = Length \times Width \times Height.[/tex]

We have all 3 dimensions already, now we can solve for the volume.

Substitute:

[tex]Volume = 3 \times 12 \times 18.[/tex]

[tex]Volume = 648in^3.[/tex]

Simone built 7 toy cars and 7 toy airplanes to make a total of 14 toys.

Simone could have built 7 toy cars and 7 toy airplanes to make a total of 14 toys.

To confirm this, we can add the number of toy cars and toy airplanes:

7 toy cars + 7 toy airplanes = 14 toys

Since Simone built the same number of toy cars and toy airplanes, dividing 14 by 2 would also give us the number of each type of toy:

14 toys ÷ 2 = 7 toys each (7 toy cars and 7 toy airplanes)

Therefore, we can conclude that Simone built 7 toy cars and 7 toy airplanes to make a total of 14 toys.

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There is no answer since we cannot take the square root of a negative trigonometry value. As a result, the issue as presented cannot be resolved.

The area of mathematics called trigonometry examines how triangle side lengths and angles relate to one another. The subject first came to light in the Hellenistic era, about in the third century BC, as a result of the use of geometry in astronomical investigations. The area of mathematics known as exact techniques deals with several trigonometric functions and possible computations using them. There are six common trigonometric functions in trigonometry. These go by the designations sine, cosine, tangent, cotangent, secant, and cosecant, respectively (csc). Trigonometry is the study of triangle characteristics, particularly those of right triangles. Consequently, studying geometry entails learning about the characteristics of all geometric forms.  

Trigonometry can be used to resolve this issue. We'll abbreviate the angle between the stairs and the slide as "".

We must first determine the slide's height. The Pythagorean Theorem allows us to perform the following:

Height 2 equals (slide length)/2 - (distance from step bottom to bottom of slide)/2 Height 2 equals 4.2/2 - 4.9/2 Height 2 equals -7.55

There is no answer since we cannot take the square root of a negative value. As a result, the issue as presented cannot be resolved.

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The density of the metal sculpture is 6.32 grams per cm³

Density can be defined as the quotient between mass and volume so we can just use the simple formula:

Density = mass/volume

And here we know the two values that we need to use as inputs in the formula above, these values are:

mass = 7.9kg

volume = 1250 cm³

We want the density in grams, then we can rewrite the mass as:

mass = 7.9kg = 7,900 g

Now just take the quotient between the two given quantities, we will get:

Density = 7,900g/1250 cm³ = 6.32 g/cm³

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Since, Consider a set of data in which the sample mean is 33. 7 and the sample standard deviation is 7. 2. Calculate the z-score given that

x= 30. 2. Therefore, the Z score is -0.486111.

Z score:

Standard scores are often referred to as z-scores; the two terms are used interchangeably. Other equivalent terms used include z-score, normal score, standardized variable, and high-energy physical attraction.

In statistics, a standard score is the number of standard deviations by which a raw score (i.e. an observation or data point) has a value greater than or less than the observed or measured mean. Raw scores above the mean have positive standard scores, while raw scores below the mean have negative standard scores.

Given that:

Sample mean (μ) = 33.7

Standard deviation (σ) = 7.2

X = 30.2

We know that:

Z score = X -μ/ σ

z-score using the formula z = (x - μ) / σ,

where,

x is your data point,

μ is the mean, and

σ is the standard deviation.

Putting the values in the equation:

⇒ Z score = X -μ/ σ

                 = 30.2 - 33.7/ 7.2

                 = -0.486111

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Answer:

cosθ = 3root58 / 58

cscθ = root58 / 7

tanθ = 7/3

Step-by-step explanation:

Draw a picture of the point. You can make a right triangle. One leg is 3 and one leg is 7. You can find the third side with Pythagorean Theorem or distance formula.

see image.

Then use right triangle trigonometry to find cosθ, cscθ, tanθ.

cosθ is the adjacent side over the hypotenuse.



cscθ is sinθ flipped over.

tanθ is opposite side over adjacent side.

see image

matrix A was expressed in the form, a=[a c] [b d] find the value of a - b + c + d. 5x+7y=7 3x-2y=9. That is

a =5, c=7; and b=3, d=-2

a - b + c + d = 5 - 3 + 7 + (- 2) = 7

The given equations are

5x + 7y = 7

3x - 2y = 9

As a matrix equation,

A = [5 7

      3 - 2]

X = [x

       y]

C = [7

      9]

That is

a =5, c=7; and b=3, d=-2

a - b + c + d = 5 - 3 + 7 + (- 2) = 7

A matrix equation is an equation of the structure Hatchet = b, where An is an m × n matrix, b is a vector in R m, and x is a vector whose coefficients x 1, x 2,..., x n are obscure.

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the complete question is :

If the following system of equations was written as a matrix equation in the form AX = C,? and matrix A was expressed in the form, a=[a c] [b d] find the value of a - b + c + d. 5x+7y=7 3x-2y=9.

The length of the rectangle is 7 units.

Length is a measure of distance or size. It is typically measured in meters, centimeters, feet, or inches. Length is a fundamental concept in mathematics, physics, and engineering. It is used to measure the size of an object or the distance between two points. Length is an important factor in the design of many structures, including buildings, bridges, and roads. Length can also be used to describe the duration of time, such as the length of a movie or a song.

To solve this problem, we will use the formula for the area of a rectangle, which is A = lw. We know that the width is the length minus 6 units, so we can rewrite the area equation as: A = (l-6)l. We then solve for l by multiplying both sides of the equation by l and dividing by l-6, giving us: l = A/(l-6). Since the area is 7 square units, we can plug in 7 for A and solve for l: l = 7/(l-6). We then solve for l by solving for the value of l on both sides of the equation, giving us: l = 7/(7-6) = 7/1 = 7. Therefore, the length of the rectangle is 7 units.

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The value of the segment MN is 18 units

Similar triangles are triangles that have the same shape but possibly different sizes in proportions

From the question, we have the following parameters that can be used in our computation:

AB=24 , AD=14 , and MQ=10.5

Given that the triangles are similar, we have the following ratio

AB : AD = MN : MQ

Substitute the known values in the above equation, so, we have the following representation

24 : 14 = MN : 10.5

Make MN the subject

MN = 10.5 * 24/14

Evaluate

MN = 18

Hence, the value of MN is 18

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Answer:

£681.95

Step-by-step explanation:

131.78% of £517.49

131.78% = 1.3178

We take

517.49 x 1.3178 = £681.95

So, the answer is £681.95

The proportion of the shaded area in the rectangle is 0.111.

The shaded area of the rectangle can be calculated by subtracting the area of the unshaded area from the total area of the rectangle. The total area of the rectangle is 36 units2 (Area = length x width). The unshaded area is 32 units2 (Area = 4 x 9). Therefore, the shaded area is 4 units2 (36-32).

The proportion of the shaded area in the rectangle can be calculated by dividing the area of the shaded area by the total area of the rectangle. The proportion of the shaded area is 4/36, or 1/9. This can also be expressed as a decimal, 0.111.

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Answer:

x>-7

Step-by-step explanation:

Answer:

angle 1 = 54° because this angle is a vertical angle of 54°, and vertican angles are always the same.

angle 2 = 126° because straight line = 180°, and there we have 54°, so 180-54=126°

angle 3 = 126° because this angle is vertical angle to 126°

angle 4 = 121° because this angle is alternative interior angle of the sum of the angles 12(54) and 67°

angle 5 = 59° because angle 5 and angle 4 makes a straight line, staring line = 180°, and 180°-angle 4(121°)= 59°

angle 6 = 121° because this anle is vertican angle of 121°

angle 7 = 59 because this angle is vertical angle of 59°

angle 8 = 59° because this angle is corresponding to angle 5 (59°), and corresponding angles are always the same

angle 9 = 54° because this angle is corresponding angle to 54°

angle 10 = 67 because angle 10, 9 and 8 creates straight line, straight line = 180°, angle 9(54) + angle 8(59)=113, and 180°-113°=67°, that means that angle 10 = 67°

angle 11 = 59 because this angle is corresponding to angle 7 (59°)

angle 12 = 54° because this angle is corresponding angle to angle 1 (54°)

that is it :)

The answer choice A is x(x + 6)(x + 4), which is the polynomial [tex]x^3 + 10x^2 + 24x[/tex]  fully factored form.

The quadratic expression enclosed in parenthesis can be factored:

x(x + 6)(x + 4)

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.[tex]x^2+x-12[/tex] is an illustration of a polynomial with a single variable.

from the question:

The given polynomial is[tex]x^3 + 10x^2 + 24x.[/tex]

From each term, we may factor out the common factor of x:

[tex]x(x^2 + 10x + 24)[/tex]

The quadratic expression enclosed in parenthesis can be factored:

x(x + 6)(x + 4)

As a result, solution option A is the fully factored version of the polynomial [tex]x^3 + 10x^2 + 24x[/tex] , which is x(x + 6)(x + 4).

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Answer:

The answer to your problem is, B. reflection across the y-axis

Step-by-step explanation:

The relation between preimage and image is defined by the rule

( x,y ) —> ( -x,y )

Reflection across y-axis represented by the above rule.

It means the △ABC is reflected across the y-axis to form​​ △A'B'C' ​.

Thus the answer to your problem is, B. reflection across the y-axis

[tex]\dfrac{\mathcal{P}_{1}}{\mathcal{P}_{2}} = \dfrac{h_{1}}{h_{2}} \iff \dfrac{37.8}{\mathcal{P}_{2}} = \dfrac{6}{15}[/tex]

[tex]\mathcal{P}_{2} = \dfrac{37.8(15)}{6} \implies \bf \mathcal{P}_{2} = 94,5 \ inches\\[/tex]

Two triangles are similar. The perimeter of the larger triangle is 94.5 inches.

SOLUTION:

Given, Two triangles are similar.  

The height of the smaller triangle is 6 inches and the corresponding height of the larger triangle is 15 inches.  

The perimeter of the smaller triangle is 37.8 inches.

We have to find what is the perimeter of the larger triangle?

We know that, for similar triangles, ratio of heights = ratio of perimeters.

[tex]\sf{Then,} \ \frac{height\ of \ 1st \ triangle}{height\ of \ 1st \ triangle} = \frac{perimeter \ of \ 2nd \ triangle}{perimeter \ of \ 2nd \ triangle}[/tex]

[tex]\sf{\frac{6}{15} =\frac{37.8}{perimeter\ of \ 2nd \ triangle}[/tex]

[tex]\sf{Perimeter} \ of \ 2^{nd \ triangle} \ \times6=37.8\times15[/tex]

[tex]\sf{Perimeter} \ of \ 2^{nd \ triangle} =37.8\times\frac{15}{6}=37.8\times\frac{5}{2} =\frac{189}{2} =94.5[/tex]

Hence, the perimeter of the larger triangle is 94.5 inches

Answer:

To determine if s is inversely proportional to f, we need to check if their product is constant. Let's multiply s and f for each row:

s * f = 0.2 * 5 = 1

s * f = 0.5 * 2 = 1

s * f = 1.4 * 0.714 ≈ 1

s * f = 7.5 * 0.133 ≈ 1

s * f = 3 * 0.3 = 0.9

As we can see, the product of s and f is approximately constant for all rows except the last one. This means that s and f are not inversely proportional in general.

However, we can see that the product of s and f is close to 1 for the first four rows. This suggests that s and f may be inversely proportional for values of s less than 3.

To confirm this, we can calculate the constant of proportionality k using the first two rows:

s * f = k

0.2 * 5 = k

k = 1

Therefore, the equation relating s and f is:

s * f = 1

or

f = 1/s

This shows that s and f are indeed inversely proportional for values of s less than 3. However, for s = 3, the product of s and f is 0.9 instead of 1, which means that s and f are not inversely proportional for this value of s.

Answer:

x = 27

Step-by-step explanation:

x - 21 = 6 ( add 21 to both sides to isolate x )

x = 27

The answer is going to be 27 as x so 27 - 21 = 6 to check you can do 6 + 21 which would equal to 27 so that’s the answer.

Therefore, x = 27

Answer:

Based on the given input-output pairs (2,8), (3,11), and (4,14), it appears that the rule for this function table is to multiply the input by 3 and then add 2 to get the output. In other words, for an input x, the output is given by the function f(x) = 3x + 2.

Answer:

categorical data

Step-by-step explanation:

thanks for the question

please mark me brainless

Answer: I believe it is categorical

If Central angle BAC of circle A measures 23/20 π T radians. Arc BC has a length of 63.48 centimeters. The radius of the circle A is: 55.2cm.

In this case, we know the length of arc BC is 63.48 cm and the central angle BAC measures 23/20 π radians.

Now let find the radius of circle A:

So:

63.48π = (23/20 π)/2π × 2πr

63.48π = 1.15 rπ

Divide both side by 1.15

r = 63.48 /1.15

r =55.2 cm

Therefore we can conclude that the radius of circle A is approximately 55.2 centimeters.

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The complete question is:

Central angle BAC of circle A measures 23/20 π T radians. Arc BC has a length of 63.48 centimeters. What is the radius of the circle? The radius of circle A is

To make a scatter plot of the data from each table, begin by assigning the x-axis to represent the values from one of the tables and the y-axis to represent the values from the other table. Then plot each pair of values onto the graph, creating a "scatter" of points. To draw a trend line, look for the general pattern in the data points and draw a line that best fits them. To find the equation of the trend line, use the formula y = mx + b, where m is the slope of the line and b is the y-intercept. To find the slope of the line, use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line. To find the y-intercept, plug the slope and any point on the line into the equation y = mx + b and solve for b.

The given data is as follows: 5, 66, and 9. We can plot these values in a scatter plot by following the steps mentioned below:Step 1: Plot the given data points on the Cartesian plane. Step 2: Find the equation of the line of best fit/trend line. We can use the least-squares regression method to find the line of best fit/trend line. This method gives us the equation of a line that best represents the relationship between two variables. In this case, the two variables are X and Y. Step 3: Draw the trend line on the scatter plot. Step 4: Write the equation of the trend line. The equation of the line of best fit/trend line is in the form of y = mx + c, where m is the slope of the line, and c is the y-intercept. . However, we can still draw a line of best fit/trend line that passes through the data points. The equation of the line of best fit/trend line can be found using the least-squares regression method. Using this method, we get the equation of the line of best fit/trend line as: y = -10.33x + 71.33Therefore, the equation of the trend line is y = -10.33x + 71.33.

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the number of coupons sent to potential members was 228.

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

According to the problem, the total number of coupons sent out was 266. Therefore, we can write an equation based on the information given:

x + 6x = 266

Simplifying and solving for x, we have:

7x = 266

x = 38

Therefore, the number of coupons sent to existing members was 38. To find the number of coupons sent to potential members, we can multiply this number by 6:

6x = 6(38) = 228

Therefore, the number of coupons sent to potential members was 228.

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The pressure on a brake pad has an area of 0.35 m² and a force of 21 N applied on it is equals to the 60N/m².

We have, area of a brake pad, A

= 0.35 m².

Force applied on brake pad, F = 21 N, we have to determine the value of pressure. Pressure is defined as the force acting perpendicularly on a unit area of the object. The standard unit of pressure is Pascals = 1 N/m². Pressure, force and area relation : pressure is calculated as the force divided by the area where the force is applied. So, in this case we have both force and area. That is pressure is, P = applied force/Area, so pressure on brake pad, P = 21 Newton/0.35 m²

=>[tex] P = \frac{2100}{35}[/tex]N/m²

=> P = 60 N/m²

Hence, the required pressure value is 60 N/m².

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Complete question:

A brake pad has an area of 0.35 m² and has a force of 21 N applied to it what’s the pressure in N/m².

Answer:

48 tiles are required.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

To solve for the area of a rectangle, we use this expression:

(Let l = length, w = width and a = area)

Inserting the dimensions of the hall:

Each tile has an area of:

To find the number of tiles needed to cover the hall, we can divide the area of the hall by the area of each tile:

Therefore, 48 tiles are required to cover the rectangular hall.